That’s the repository where physicists post their latest work, usually before it is published (if it ever gets published at all). Free from the pernicious peer review process that purifies prestigious professional publications, the arXiv offers a way for the wayward to expose their way-out views.

In the old days, the arXiv web address was xxx.lanl.gov (still a mirror site) and not just because some of the papers were about naked quasars. It is the place to go to see physics in the raw. Alongside papers residing fully within the borders of mainstream physics you could find numerous not-even-half-microwaved ideas for explaining everything from supernovas to superheroes. And arXiv.org remains to this day the best place to look for innovative speculations about how to solve physics’ most persistent problems.

Nobody doubts that physics faces some formidable problems that require imaginative thinking. But experts are divided on whether success will come from strategies rooted in the standard dogma, or will require paradigm-busting revolutions.

It’s possible, perhaps, that current crises in physics will be resolved with radical ideas that challenge standard views while remaining somewhere in the vicinity of the standard physics box. Consider, for instance, some recent attempts to solve what physicists call the cosmological constant problem.

Einstein proposed the idea of a cosmological constant — an energy field with constant density throughout the vacuum of space — in 1917. Such an energy field would exert a repulsive force on space itself; Einstein thought the universe needed it to keep from collapsing. But then astronomers figured out that the universe is expanding, and Einstein decided his idea didn’t work very well anyway.

It turned out, though, that the vacuum really should be full of energy, because quantum mechanics permits (actually, requires) energetic particles to pop into and out of existence in space all the time. These “virtual” particles infuse space with energy. Enough energy, in fact, to make the universe expand so fast that galaxies and stars could never have formed. Since galaxies and stars have formed, physicists reasoned that the cosmological constant must be canceled out by something else.

Then in 1998, astronomers shocked physics fans everywhere by discovering that the universe is expanding at an accelerating rate. Therefore there must be a cosmological constant (or some other type of vacuum energy) in space after all. It’s just a lot weaker than the calculations said it should be. Nobody has yet been able to explain, to anyone else’s satisfaction, why this vacuum energy is as flimsy as it is.

“The problem is not that the vacuum energy has been found; there was already a problem when it was thought to be unobservably small,” writes physicist C.P. Burgess of the Perimeter Institute for Theoretical Physics in Waterloo, Canada. “The problem is that we believe the vacuum energy can be computed, and the result should be enormous compared with what has been measured.”

Burgess discusses the cosmological constant problem at length in a paper available (naturally) at arXiv.org. He suggests one possible solution that is not only out of the box, but is literally out of any (three-dimensional) box.

If space possesses more than the standard three dimensions, Burgess says, then vacuum energy might in fact be very strong. But the impact of that vacuum energy would be diluted. In other words, the high-powered vacuum energy could operate in dimensions that we cannot see, with only a little leakage left over to accelerate the expansion of the universe.

These extra dimensions would need to be huge by subatomic standards — something on the scale of a micrometer. Their presence might be detected, though, by ultrasensitive tests of the strength of gravity at micrometer distances.

Venturing even farther outside the box is Dragan Hajdukovic of CERN (the European physics lab in Geneva) and the Institute of Physics, Astrophysics and Cosmology in Cetinje, Montenegro. His paper presents calculations suggesting that humongous vacuum energy can be reconciled with observation by adding a correction factor to the equations. He thinks this factor might have something to do with pions, subatomic particles made of a quark combined with an antiquark.

Suppose, he argues, that antimatter has the opposite gravitational effect of matter (unlikely, perhaps, but still a topic of experimental investigation). Then pions would be “gravitational dipoles,” with positive gravity on one end and negative gravity on the other, like the opposite poles of a magnet. His calculations suggest that such gravitational dipoles could explain not only the amount of observed vacuum energy, but also the apparent presence of “dark matter” in space that scientists have so far been unable to identify.

The odds of either of these ideas being right are roughly similar to the chances that a collection of tweets from Twitter will win next year’s Pulitzer Prize. And faithful arXiv readers know you could find hundreds of other similarly speculative proposals in the arXiv archive.

But the problems these proposals address have proven hard to solve. So it may even be that these particular ideas aren’t radical enough. Such crazy ideas are rarely right, but it’s a reasonably good bet that the eventual correct solution to the cosmological constant will appear, at first glance, to be among the craziest.

“Most challenges to scientific orthodoxy are wrong,” the Nobel laureate physicist Murray Gell-Mann once said. “A lot of them are crank. But it happens from time to time that a challenge to scientific orthodoxy is actually right.”